Theorems · Theorem · commutative algebra
PowerSeries.subst_tsum
∀ {R : Type u_2} [inst : CommRing R] {τ : Type u_3} {S : Type u_4} [inst_1 : CommRing S] [inst_2 : Algebra R S]
{x : ℕ → PowerSeries R} {a : MvPowerSeries τ S} [inst_3 : UniformSpace R] [DiscreteUniformity R]
[inst_5 : UniformSpace S] [DiscreteUniformity S],
Summable x → PowerSeries.HasSubst a → PowerSeries.subst a (∑' (i : ℕ), x i) = ∑' (i : ℕ), PowerSeries.subst a (x i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- AlgHomproof · cited by 3,236
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- tsumstatement and proof · cited by 1,148
- PowerSeriesstatement and proof · cited by 797
- Summablestatement and proof · cited by 778
- MvPowerSeriesstatement and proof · cited by 659
- PowerSeries.HasSubststatement and proof · cited by 67
- PowerSeries.subststatement · cited by 58
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